# Successive numbers starting from #1# are written in a rectangular grid, starting in the top left corner and snaking down diagonally to the right as shown. In which row and column does #2008# occur?

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#color(white)(0)1color(white)(00)2color(white)(00)6color(white)(00)7color(white)(0)15color(white)(0)16#

#color(white)(0)3color(white)(00)5color(white)(00)8color(white)(0)14color(white)(0)"etc"#

#color(white)(0)4color(white)(00)9color(white)(0)13#

#10color(white)(0)12#

#11#

##### 1 Answer

The

#### Explanation:

The last number added to the

What is the smallest triangular number greater than or equal to

Given:

#1/2n(n+1) = T_n >= 2008#

Multiply both ends by

#n(n+1) >= 4016#

So the value of

#T_63 = 1/2*63*64 = 2016#

#T_62 = 1/2*62*63 = 1953#

So

Note that due to the boustrophedonic (like an ox ploughing a field) way in which the numbers are written,